In the most general case, the field can be coupled both to the curvature and to matter fields present in the theory. By means of Weyl (or conformal) transformation of the metric tensor one can always choose a parametrization, in which the scalar field is non-minimally coupled only to either the gravitational or matter part of the action functional. Different parametrizations are called 'conformal frames', and two most commonly used in the literature are Einstein frame, with the field coupled to matter, and Jordan frame, where non-minimal coupling to curvature is present [1]}, [2]}. Usually, Weyl transformations are used as a mathematical tool, allowing one to choose a frame in which the calculations are easier, and then transforming back to the frame considered to be physical. There is no agreement as to which frame is the right one, various arguments in favour of either can be found in the literature [3]}-[4]}. Some authors, however, claim that all conformally-related frames are in fact different representations of the same physical theory, and all quantities that can be connected to observations should be expressed in terms of variables invariant under Weyl rescaling [5]}, [6]}.
